TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11803
AB  - Optical vortex is a coherent localized structure carrying energy around the pivot point. It is characterized by an optical angular momentum (OAM) mathematically described by azimuthal phase term exp(ilφ). Here, the integer number l stands for the winding number or topological charge of the vortex [1]. Particularly interesting are vortices generated in discrete systems [2]. They are specified by quantized topological charge and exhibit inherent robustness on perturbations within the system [3]. One of the structures that support discrete vortices is multi-core fiber (MCF) [4]. Here, we study MCF structure composed of two concentric hexagonal rings, A and B (Fig. 1). Beside equal coupling constants among nearest sites of A and B ring, we also consider a presence of artificial flux (Φ) which affects coupling between sites in the A ring [5]. The presence of artificial flux does not change the topological charge of vortices, only shifts their corresponding eigenvalues. Moreover, vortex excitation in one of the rings produces a regular periodical energy exchange between A and B rings in a form of stable breathing coupled-vortex structure. In passive MCF the vortex excitation is necessary to propagate vortex through the system. However, including the saturable gain and linear loss in the MCF, the vortices of different topological charge can be excited even from the uniform background by tuning the flux value. Numerical simulations show high robustness of newly formed vortices, which offers possibility to utilize the proposed setup as highly controllable vortex generator. Moreover, this can be of particular importance in the ring array based lasers [6,7].
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2023 : 9th International School and Conference on Photonics : book of abstracts; August 28 - September 1, 2023; Belgrade
T1  - Coupled vortex generator in active multi-core fibers
SP  - 53
EP  - 53
UR  - https://hdl.handle.net/21.15107/rcub_vinar_11803
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra",
year = "2023",
abstract = "Optical vortex is a coherent localized structure carrying energy around the pivot point. It is characterized by an optical angular momentum (OAM) mathematically described by azimuthal phase term exp(ilφ). Here, the integer number l stands for the winding number or topological charge of the vortex [1]. Particularly interesting are vortices generated in discrete systems [2]. They are specified by quantized topological charge and exhibit inherent robustness on perturbations within the system [3]. One of the structures that support discrete vortices is multi-core fiber (MCF) [4]. Here, we study MCF structure composed of two concentric hexagonal rings, A and B (Fig. 1). Beside equal coupling constants among nearest sites of A and B ring, we also consider a presence of artificial flux (Φ) which affects coupling between sites in the A ring [5]. The presence of artificial flux does not change the topological charge of vortices, only shifts their corresponding eigenvalues. Moreover, vortex excitation in one of the rings produces a regular periodical energy exchange between A and B rings in a form of stable breathing coupled-vortex structure. In passive MCF the vortex excitation is necessary to propagate vortex through the system. However, including the saturable gain and linear loss in the MCF, the vortices of different topological charge can be excited even from the uniform background by tuning the flux value. Numerical simulations show high robustness of newly formed vortices, which offers possibility to utilize the proposed setup as highly controllable vortex generator. Moreover, this can be of particular importance in the ring array based lasers [6,7].",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2023 : 9th International School and Conference on Photonics : book of abstracts; August 28 - September 1, 2023; Belgrade",
title = "Coupled vortex generator in active multi-core fibers",
pages = "53-53",
url = "https://hdl.handle.net/21.15107/rcub_vinar_11803"
}

Beličev, P., Gligorić, G.,& Maluckov, A.. (2023). Coupled vortex generator in active multi-core fibers. in PHOTONICA2023 : 9th International School and Conference on Photonics : book of abstracts; August 28 - September 1, 2023; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 53-53.
https://hdl.handle.net/21.15107/rcub_vinar_11803

Beličev P, Gligorić G, Maluckov A. Coupled vortex generator in active multi-core fibers. in PHOTONICA2023 : 9th International School and Conference on Photonics : book of abstracts; August 28 - September 1, 2023; Belgrade. 2023;:53-53.
https://hdl.handle.net/21.15107/rcub_vinar_11803 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, "Coupled vortex generator in active multi-core fibers" in PHOTONICA2023 : 9th International School and Conference on Photonics : book of abstracts; August 28 - September 1, 2023; Belgrade (2023):53-53,
https://hdl.handle.net/21.15107/rcub_vinar_11803 .

TY  - JOUR
AU  - Stojanović, Danka B.
AU  - Gligorić, Goran
AU  - Beličev, Petra
AU  - Belić, Milivoj R.
AU  - Hadžievski, Ljupčo
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9769
AB  - In this article, we propose a chiral metamaterial absorber based on four rotated twisted closed ring resonators operative in terahertz frequency range. The resonant features are analyzed by electric field amplitude distributions, and surface currents flow generated by the interaction of circularly polarized waves with the chiral structure. The highest field amplitudes at the fundamental resonance are obtained at the gap region of the resonator. Therefore, the efficiency of the proposed absorber is determined through response of absorption spectrum around this resonance with variation of geometrical parameters of the structure. Significant increase of absorption of the left circularly polarized light is obtained with variation of the period size of structure. Consequently, huge circular dichroism, and near-unity polarization selective absorption have been provided. This makes the proposed chiral structure a good candidate for designing circular polarization selective absorber. © 2020 IEEE.
T2  - IEEE Journal of Selected Topics in Quantum Electronics
T2  - IEEE Journal of Selected Topics in Quantum Electronics
T1  - Circular polarization selective metamaterial absorber in terahertz frequency range
VL  - 27
IS  - 1
DO  - 10.1109/JSTQE.2020.3024570
ER  - 

@article{
author = "Stojanović, Danka B. and Gligorić, Goran and Beličev, Petra and Belić, Milivoj R. and Hadžievski, Ljupčo",
year = "2021",
abstract = "In this article, we propose a chiral metamaterial absorber based on four rotated twisted closed ring resonators operative in terahertz frequency range. The resonant features are analyzed by electric field amplitude distributions, and surface currents flow generated by the interaction of circularly polarized waves with the chiral structure. The highest field amplitudes at the fundamental resonance are obtained at the gap region of the resonator. Therefore, the efficiency of the proposed absorber is determined through response of absorption spectrum around this resonance with variation of geometrical parameters of the structure. Significant increase of absorption of the left circularly polarized light is obtained with variation of the period size of structure. Consequently, huge circular dichroism, and near-unity polarization selective absorption have been provided. This makes the proposed chiral structure a good candidate for designing circular polarization selective absorber. © 2020 IEEE.",
journal = "IEEE Journal of Selected Topics in Quantum Electronics, IEEE Journal of Selected Topics in Quantum Electronics",
title = "Circular polarization selective metamaterial absorber in terahertz frequency range",
volume = "27",
number = "1",
doi = "10.1109/JSTQE.2020.3024570"
}

Stojanović, D. B., Gligorić, G., Beličev, P., Belić, M. R.,& Hadžievski, L.. (2021). Circular polarization selective metamaterial absorber in terahertz frequency range. in IEEE Journal of Selected Topics in Quantum Electronics, 27(1).
https://doi.org/10.1109/JSTQE.2020.3024570

Stojanović DB, Gligorić G, Beličev P, Belić MR, Hadžievski L. Circular polarization selective metamaterial absorber in terahertz frequency range. in IEEE Journal of Selected Topics in Quantum Electronics. 2021;27(1).
doi:10.1109/JSTQE.2020.3024570 .

Stojanović, Danka B., Gligorić, Goran, Beličev, Petra, Belić, Milivoj R., Hadžievski, Ljupčo, "Circular polarization selective metamaterial absorber in terahertz frequency range" in IEEE Journal of Selected Topics in Quantum Electronics, 27, no. 1 (2021),
https://doi.org/10.1109/JSTQE.2020.3024570 . .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Turitsyn, Sergei
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9869
AB  - Topological properties can make light field remarkably robust to various external perturbations. The ability to control and change on demand topological characteristics of light paves the way to new interesting physical phenomena and applications. Here, numerical modelling design of the device based on active multi-core fiber that can change topological charge of the state of light has been proposed. The concept is based on the nonlinear dynamics of optical vortices in active multi-core optical fiber with linearly coupled cores, saturated gain, and constant linear losses. Results demonstrate that the proposed system can provide change of the topological charge of vortices.
T2  - Annalen der Physik
T1  - Topological charge switch in active multi-core fibers
VL  - 533
IS  - 9
SP  - 2100108
DO  - 10.1002/andp.202100108
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Turitsyn, Sergei",
year = "2021",
abstract = "Topological properties can make light field remarkably robust to various external perturbations. The ability to control and change on demand topological characteristics of light paves the way to new interesting physical phenomena and applications. Here, numerical modelling design of the device based on active multi-core fiber that can change topological charge of the state of light has been proposed. The concept is based on the nonlinear dynamics of optical vortices in active multi-core optical fiber with linearly coupled cores, saturated gain, and constant linear losses. Results demonstrate that the proposed system can provide change of the topological charge of vortices.",
journal = "Annalen der Physik",
title = "Topological charge switch in active multi-core fibers",
volume = "533",
number = "9",
pages = "2100108",
doi = "10.1002/andp.202100108"
}

Beličev, P., Gligorić, G., Maluckov, A., Hadžievski, L.,& Turitsyn, S.. (2021). Topological charge switch in active multi-core fibers. in Annalen der Physik, 533(9), 2100108.
https://doi.org/10.1002/andp.202100108

Beličev P, Gligorić G, Maluckov A, Hadžievski L, Turitsyn S. Topological charge switch in active multi-core fibers. in Annalen der Physik. 2021;533(9):2100108.
doi:10.1002/andp.202100108 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Turitsyn, Sergei, "Topological charge switch in active multi-core fibers" in Annalen der Physik, 533, no. 9 (2021):2100108,
https://doi.org/10.1002/andp.202100108 . .

TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Turitsyn, S.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10901
AB  - The multi-core fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, the MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division-multiplexing in high capacity fiber-optic communication systems which may also be attractive for applications in high power lasers. Up to now, the main concern of our study has been related to optimization of the conditions capable to ensure transfer of high coherent light through the MCFs [1]. Regarding this we firstly proved the possibility of nonlinearity managed propagation of highly coherent vortices carrying huge power through the passive circular MCFs, which consist of small number of periphery cores. The central core has been shown to play the role of optional switch/gate of coherent light transfer [1]. In addition, the effects of the presence of central core and material loss/gain of all cores on the linear MCF system eigenvalue commensurability conditions have shown significant impact on the coherent planar and vortex mode dynamics [2]. All these findings stimulated the investigation of possibility to amplify the power transferred through the MCF via vortex carriers by inducing effects of the saturable gain and non-saturable loss in the periphery and/or central cores [3]. We numerically consider three cases of active circular MCFs. In the first case active were only periphery cores. Secondly, we investigated response of the system with only central core active, while the last case included all cores to be active. The light propagation is modeled by the generalized nonlinear difference-differential Schrödinger equations with complex coefficients and saturable gain [3]. Results for MCF with 4, 5 and 6 periphery cores have shown that the active periphery is the most promising candidate for topological charge switch of vortices carrying high powers [4]. In this specific operating regime, MCF provides change of the vortex topological charge value, i.e. transition between different vortex states. Moreover, presented system supports topological charge switch function between noncounterpart vortices by proper tailoring the ratio between gain and loss in periphery. The key condition for this phenomenon is existence of the central core which appears to play role of mode dynamics moderator. Being the ‘singular phase’ point of vortex, the central core which only passively takes part in tunneling energy towards the periphery cores, can support the coherent light amplification through the MCF. On the top of this, presented system shows to be a promising platform for practical realization of devices covering range of multiple functions in applications: from high-power fiber lasers to coherent beam combiners and selective carriers of vortex beams.
PB  - Belgrade : Institute of Physics Belgrade
C3  - PHOTONICA2021 : 8th International School and Conference on Photonics and HEMMAGINERO workshop : Abstracts of Tutorial, Keynote, Invited Lectures, Progress Reports and Contributed Papers; August 23-27, 2021; Belgrade
T1  - Active multi-core fibers – photonic platform for development of a topological charge switching device
SP  - 71
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10901
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Turitsyn, S.",
year = "2021",
abstract = "The multi-core fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, the MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division-multiplexing in high capacity fiber-optic communication systems which may also be attractive for applications in high power lasers. Up to now, the main concern of our study has been related to optimization of the conditions capable to ensure transfer of high coherent light through the MCFs [1]. Regarding this we firstly proved the possibility of nonlinearity managed propagation of highly coherent vortices carrying huge power through the passive circular MCFs, which consist of small number of periphery cores. The central core has been shown to play the role of optional switch/gate of coherent light transfer [1]. In addition, the effects of the presence of central core and material loss/gain of all cores on the linear MCF system eigenvalue commensurability conditions have shown significant impact on the coherent planar and vortex mode dynamics [2]. All these findings stimulated the investigation of possibility to amplify the power transferred through the MCF via vortex carriers by inducing effects of the saturable gain and non-saturable loss in the periphery and/or central cores [3]. We numerically consider three cases of active circular MCFs. In the first case active were only periphery cores. Secondly, we investigated response of the system with only central core active, while the last case included all cores to be active. The light propagation is modeled by the generalized nonlinear difference-differential Schrödinger equations with complex coefficients and saturable gain [3]. Results for MCF with 4, 5 and 6 periphery cores have shown that the active periphery is the most promising candidate for topological charge switch of vortices carrying high powers [4]. In this specific operating regime, MCF provides change of the vortex topological charge value, i.e. transition between different vortex states. Moreover, presented system supports topological charge switch function between noncounterpart vortices by proper tailoring the ratio between gain and loss in periphery. The key condition for this phenomenon is existence of the central core which appears to play role of mode dynamics moderator. Being the ‘singular phase’ point of vortex, the central core which only passively takes part in tunneling energy towards the periphery cores, can support the coherent light amplification through the MCF. On the top of this, presented system shows to be a promising platform for practical realization of devices covering range of multiple functions in applications: from high-power fiber lasers to coherent beam combiners and selective carriers of vortex beams.",
publisher = "Belgrade : Institute of Physics Belgrade",
journal = "PHOTONICA2021 : 8th International School and Conference on Photonics and HEMMAGINERO workshop : Abstracts of Tutorial, Keynote, Invited Lectures, Progress Reports and Contributed Papers; August 23-27, 2021; Belgrade",
title = "Active multi-core fibers – photonic platform for development of a topological charge switching device",
pages = "71",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10901"
}

Beličev, P., Gligorić, G., Maluckov, A., Hadžievski, L.,& Turitsyn, S.. (2021). Active multi-core fibers – photonic platform for development of a topological charge switching device. in PHOTONICA2021 : 8th International School and Conference on Photonics and HEMMAGINERO workshop : Abstracts of Tutorial, Keynote, Invited Lectures, Progress Reports and Contributed Papers; August 23-27, 2021; Belgrade
Belgrade : Institute of Physics Belgrade., 71.
https://hdl.handle.net/21.15107/rcub_vinar_10901

Beličev P, Gligorić G, Maluckov A, Hadžievski L, Turitsyn S. Active multi-core fibers – photonic platform for development of a topological charge switching device. in PHOTONICA2021 : 8th International School and Conference on Photonics and HEMMAGINERO workshop : Abstracts of Tutorial, Keynote, Invited Lectures, Progress Reports and Contributed Papers; August 23-27, 2021; Belgrade. 2021;:71.
https://hdl.handle.net/21.15107/rcub_vinar_10901 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Turitsyn, S., "Active multi-core fibers – photonic platform for development of a topological charge switching device" in PHOTONICA2021 : 8th International School and Conference on Photonics and HEMMAGINERO workshop : Abstracts of Tutorial, Keynote, Invited Lectures, Progress Reports and Contributed Papers; August 23-27, 2021; Belgrade (2021):71,
https://hdl.handle.net/21.15107/rcub_vinar_10901 .

TY  - JOUR
AU  - Stojanović, Danka
AU  - Beličev, Petra
AU  - Radovanović, Jelena V.
AU  - Milanović, Vitomir B.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8542
AB  - In this work, we have systematically studied the impact of geometric parameters on chiral effects which occur in metamaterial made of Ω elements. The analysis of group delays and electric field enhancements indicate stronger interaction between the structure and right circularly polarized waves. Calculations of optical activity and circular dichroism for different values of geometric parameters, allow us to deduce that the thickness of the wire and the gap size have large influence on these effects. On the other hand, the radius of the wire affects mainly the resonant frequency position which enables frequency tunability. The results indicate that multi-functional design of this chiral metamaterial offers great flexibility for various devices: enantiomeric sensors, circular polarizers and light modulators. © 2019 Elsevier B.V.
T2  - Physics Letters A
T1  - Numerical parametric study of chiral effects and group delays in Ω element based terahertz metamaterial
VL  - 383
IS  - 15
SP  - 1816
EP  - 1820
DO  - 10.1016/j.physleta.2019.02.035
ER  - 

@article{
author = "Stojanović, Danka and Beličev, Petra and Radovanović, Jelena V. and Milanović, Vitomir B.",
year = "2019",
abstract = "In this work, we have systematically studied the impact of geometric parameters on chiral effects which occur in metamaterial made of Ω elements. The analysis of group delays and electric field enhancements indicate stronger interaction between the structure and right circularly polarized waves. Calculations of optical activity and circular dichroism for different values of geometric parameters, allow us to deduce that the thickness of the wire and the gap size have large influence on these effects. On the other hand, the radius of the wire affects mainly the resonant frequency position which enables frequency tunability. The results indicate that multi-functional design of this chiral metamaterial offers great flexibility for various devices: enantiomeric sensors, circular polarizers and light modulators. © 2019 Elsevier B.V.",
journal = "Physics Letters A",
title = "Numerical parametric study of chiral effects and group delays in Ω element based terahertz metamaterial",
volume = "383",
number = "15",
pages = "1816-1820",
doi = "10.1016/j.physleta.2019.02.035"
}

Stojanović, D., Beličev, P., Radovanović, J. V.,& Milanović, V. B.. (2019). Numerical parametric study of chiral effects and group delays in Ω element based terahertz metamaterial. in Physics Letters A, 383(15), 1816-1820.
https://doi.org/10.1016/j.physleta.2019.02.035

Stojanović D, Beličev P, Radovanović JV, Milanović VB. Numerical parametric study of chiral effects and group delays in Ω element based terahertz metamaterial. in Physics Letters A. 2019;383(15):1816-1820.
doi:10.1016/j.physleta.2019.02.035 .

Stojanović, Danka, Beličev, Petra, Radovanović, Jelena V., Milanović, Vitomir B., "Numerical parametric study of chiral effects and group delays in Ω element based terahertz metamaterial" in Physics Letters A, 383, no. 15 (2019):1816-1820,
https://doi.org/10.1016/j.physleta.2019.02.035 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Beličev, Petra
AU  - Leykam, Daniel
AU  - Maluckov, Aleksandra
PY  - 2019
UR  - https://link.aps.org/doi/10.1103/PhysRevA.99.013826
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8035
AB  - We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays. © 2019 American Physical Society.
T2  - Physical Review A
T1  - Nonlinear symmetry breaking of Aharonov-Bohm cages
VL  - 99
IS  - 1
SP  - 013826
DO  - 10.1103/PhysRevA.99.013826
ER  - 

@article{
author = "Gligorić, Goran and Beličev, Petra and Leykam, Daniel and Maluckov, Aleksandra",
year = "2019",
abstract = "We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays. © 2019 American Physical Society.",
journal = "Physical Review A",
title = "Nonlinear symmetry breaking of Aharonov-Bohm cages",
volume = "99",
number = "1",
pages = "013826",
doi = "10.1103/PhysRevA.99.013826"
}

Gligorić, G., Beličev, P., Leykam, D.,& Maluckov, A.. (2019). Nonlinear symmetry breaking of Aharonov-Bohm cages. in Physical Review A, 99(1), 013826.
https://doi.org/10.1103/PhysRevA.99.013826

Gligorić G, Beličev P, Leykam D, Maluckov A. Nonlinear symmetry breaking of Aharonov-Bohm cages. in Physical Review A. 2019;99(1):013826.
doi:10.1103/PhysRevA.99.013826 .

Gligorić, Goran, Beličev, Petra, Leykam, Daniel, Maluckov, Aleksandra, "Nonlinear symmetry breaking of Aharonov-Bohm cages" in Physical Review A, 99, no. 1 (2019):013826,
https://doi.org/10.1103/PhysRevA.99.013826 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Beličev, Petra
AU  - Leykam, Daniel
AU  - Maluckov, Aleksandra
PY  - 2019
UR  - https://link.aps.org/doi/10.1103/PhysRevA.99.013826
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8035
UR  - https://arxiv.org/pdf/1810.01618.pdf
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8039
AB  - We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays. © 2019 American Physical Society.
T2  - Physical Review A
T1  - Nonlinear symmetry breaking of Aharonov-Bohm cages
VL  - 99
IS  - 1
SP  - 013826
DO  - 10.1103/PhysRevA.99.013826
ER  - 

@article{
author = "Gligorić, Goran and Beličev, Petra and Leykam, Daniel and Maluckov, Aleksandra",
year = "2019",
abstract = "We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays. © 2019 American Physical Society.",
journal = "Physical Review A",
title = "Nonlinear symmetry breaking of Aharonov-Bohm cages",
volume = "99",
number = "1",
pages = "013826",
doi = "10.1103/PhysRevA.99.013826"
}

Gligorić, G., Beličev, P., Leykam, D.,& Maluckov, A.. (2019). Nonlinear symmetry breaking of Aharonov-Bohm cages. in Physical Review A, 99(1), 013826.
https://doi.org/10.1103/PhysRevA.99.013826

Gligorić G, Beličev P, Leykam D, Maluckov A. Nonlinear symmetry breaking of Aharonov-Bohm cages. in Physical Review A. 2019;99(1):013826.
doi:10.1103/PhysRevA.99.013826 .

Gligorić, Goran, Beličev, Petra, Leykam, Daniel, Maluckov, Aleksandra, "Nonlinear symmetry breaking of Aharonov-Bohm cages" in Physical Review A, 99, no. 1 (2019):013826,
https://doi.org/10.1103/PhysRevA.99.013826 . .

TY  - JOUR
AU  - Johansson, Magnus M.
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Gulevich, Dmitry R.
AU  - Skryabin, Dmitry V.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8815
AB  - We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin–orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. © 2019 The Author(s).
T2  - Journal of Physics Communications
T1  - Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains
VL  - 3
IS  - 1
SP  - 015001
DO  - 10.1088/2399-6528/aaf7c9
ER  - 

@article{
author = "Johansson, Magnus M. and Beličev, Petra and Gligorić, Goran and Gulevich, Dmitry R. and Skryabin, Dmitry V.",
year = "2019",
abstract = "We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin–orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. © 2019 The Author(s).",
journal = "Journal of Physics Communications",
title = "Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains",
volume = "3",
number = "1",
pages = "015001",
doi = "10.1088/2399-6528/aaf7c9"
}

Johansson, M. M., Beličev, P., Gligorić, G., Gulevich, D. R.,& Skryabin, D. V.. (2019). Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains. in Journal of Physics Communications, 3(1), 015001.
https://doi.org/10.1088/2399-6528/aaf7c9

Johansson MM, Beličev P, Gligorić G, Gulevich DR, Skryabin DV. Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains. in Journal of Physics Communications. 2019;3(1):015001.
doi:10.1088/2399-6528/aaf7c9 .

Johansson, Magnus M., Beličev, Petra, Gligorić, Goran, Gulevich, Dmitry R., Skryabin, Dmitry V., "Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains" in Journal of Physics Communications, 3, no. 1 (2019):015001,
https://doi.org/10.1088/2399-6528/aaf7c9 . .

TY  - JOUR
AU  - Stojanović, Danka
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Hadžievski, Ljupčo
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1909
AB  - We present a chiral metamaterial (CMM) made of periodically distributed compact elements in a form of twisted closed ring resonators designed to be operational in terahertz (THz) frequency range. We analyze the three observed resonances in the absorption spectra and electric field distribution of linearly polarized incident electromagnetic waves. It has been shown that they arise due to excitation of symmetric and antisymmetric modes and are dependent on the geometry of resonant elements as well as the periodicity of the system. For the case of incident circularly polarized waves, a phenomenon of circular dichroism was observed, and its origin and dependency on the geometrical parameters and metal and dielectric losses was examined. This study indicates that the proposed CMM has a high potential for applications in the design of different THz components.
T2  - Journal of Physics. D: Applied Physics
T1  - Terahertz chiral metamaterial based on twisted closed ring resonators
VL  - 51
IS  - 4
DO  - 10.1088/1361-6463/aaa06d
ER  - 

@article{
author = "Stojanović, Danka and Beličev, Petra and Gligorić, Goran and Hadžievski, Ljupčo",
year = "2018",
abstract = "We present a chiral metamaterial (CMM) made of periodically distributed compact elements in a form of twisted closed ring resonators designed to be operational in terahertz (THz) frequency range. We analyze the three observed resonances in the absorption spectra and electric field distribution of linearly polarized incident electromagnetic waves. It has been shown that they arise due to excitation of symmetric and antisymmetric modes and are dependent on the geometry of resonant elements as well as the periodicity of the system. For the case of incident circularly polarized waves, a phenomenon of circular dichroism was observed, and its origin and dependency on the geometrical parameters and metal and dielectric losses was examined. This study indicates that the proposed CMM has a high potential for applications in the design of different THz components.",
journal = "Journal of Physics. D: Applied Physics",
title = "Terahertz chiral metamaterial based on twisted closed ring resonators",
volume = "51",
number = "4",
doi = "10.1088/1361-6463/aaa06d"
}

Stojanović, D., Beličev, P., Gligorić, G.,& Hadžievski, L.. (2018). Terahertz chiral metamaterial based on twisted closed ring resonators. in Journal of Physics. D: Applied Physics, 51(4).
https://doi.org/10.1088/1361-6463/aaa06d

Stojanović D, Beličev P, Gligorić G, Hadžievski L. Terahertz chiral metamaterial based on twisted closed ring resonators. in Journal of Physics. D: Applied Physics. 2018;51(4).
doi:10.1088/1361-6463/aaa06d .

Stojanović, Danka, Beličev, Petra, Gligorić, Goran, Hadžievski, Ljupčo, "Terahertz chiral metamaterial based on twisted closed ring resonators" in Journal of Physics. D: Applied Physics, 51, no. 4 (2018),
https://doi.org/10.1088/1361-6463/aaa06d . .

TY  - CONF
AU  - Stojanović, Danka B.
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Hadžievski, Ljupčo
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12735
AB  - Chiral metamaterial consists of periodically placed resonant elements exhibiting chiral effects such as circular dichroism and optical activity. They appear due to the coupling of electric and magnetic fields which is result of an interaction of electromagnetic wave and chiral metamaterial. Numerous designs of chiral resonant elements are proposed providing applications for polarization conversion, filtering and absorption in THz frequency range [1, 2]. Here, we analyze propagation of electromagnetic waves through chiral metamaterial composed of twisted closed ring resonators (TCRR). The proposed chiral metamaterial is ultrathin structure which makes this design easy to fabricate and, at the same time, maintains effects which can be observed in conventional chiral 3D metamaterial structures. Dimensions of chiral elements are chosen to provide resonances within THz frequency range. Different geometrical parameters are varied in order to determine their influence on resonant frequency and losses [3]. For our TCRR chiral metamaterial structure, the analysis is made from microscopic as well as from macroscopic point of view. Through numerical simulations, we calculate electromagnetic field distribution, scattering coefficients, absorption and consequently, circular dichroism. Additionally, we examine losses in our chiral structure in terms of radiative and non-radiative ones [4] and explore its influence on the circular dichroism.
PB  - Belgrade : Institute of Physics Belgrade
C3  - PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
T1  - Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators
SP  - 190
EP  - 190
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12735
ER  - 

@conference{
author = "Stojanović, Danka B. and Beličev, Petra and Gligorić, Goran and Hadžievski, Ljupčo",
year = "2017",
abstract = "Chiral metamaterial consists of periodically placed resonant elements exhibiting chiral effects such as circular dichroism and optical activity. They appear due to the coupling of electric and magnetic fields which is result of an interaction of electromagnetic wave and chiral metamaterial. Numerous designs of chiral resonant elements are proposed providing applications for polarization conversion, filtering and absorption in THz frequency range [1, 2]. Here, we analyze propagation of electromagnetic waves through chiral metamaterial composed of twisted closed ring resonators (TCRR). The proposed chiral metamaterial is ultrathin structure which makes this design easy to fabricate and, at the same time, maintains effects which can be observed in conventional chiral 3D metamaterial structures. Dimensions of chiral elements are chosen to provide resonances within THz frequency range. Different geometrical parameters are varied in order to determine their influence on resonant frequency and losses [3]. For our TCRR chiral metamaterial structure, the analysis is made from microscopic as well as from macroscopic point of view. Through numerical simulations, we calculate electromagnetic field distribution, scattering coefficients, absorption and consequently, circular dichroism. Additionally, we examine losses in our chiral structure in terms of radiative and non-radiative ones [4] and explore its influence on the circular dichroism.",
publisher = "Belgrade : Institute of Physics Belgrade",
journal = "PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts",
title = "Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators",
pages = "190-190",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12735"
}

Stojanović, D. B., Beličev, P., Gligorić, G.,& Hadžievski, L.. (2017). Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
Belgrade : Institute of Physics Belgrade., 190-190.
https://hdl.handle.net/21.15107/rcub_vinar_12735

Stojanović DB, Beličev P, Gligorić G, Hadžievski L. Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts. 2017;:190-190.
https://hdl.handle.net/21.15107/rcub_vinar_12735 .

Stojanović, Danka B., Beličev, Petra, Gligorić, Goran, Hadžievski, Ljupčo, "Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators" in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts (2017):190-190,
https://hdl.handle.net/21.15107/rcub_vinar_12735 .

TY  - CONF
AU  - Stojanović, Danka B.
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Radovanović, Jelena V.
AU  - Milanović, Vitomir B.
AU  - Hadžievski, Ljupčo
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12789
PB  - Belgrade : Institute of physics
C3  - 10th Photonics Workshop : Book of abstracts
T1  - Electromagnetic wave propagation through terahertz chiral metamaterials
SP  - 9
EP  - 9
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12789
ER  - 

@conference{
author = "Stojanović, Danka B. and Beličev, Petra and Gligorić, Goran and Radovanović, Jelena V. and Milanović, Vitomir B. and Hadžievski, Ljupčo",
year = "2017",
publisher = "Belgrade : Institute of physics",
journal = "10th Photonics Workshop : Book of abstracts",
title = "Electromagnetic wave propagation through terahertz chiral metamaterials",
pages = "9-9",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12789"
}

Stojanović, D. B., Beličev, P., Gligorić, G., Radovanović, J. V., Milanović, V. B.,& Hadžievski, L.. (2017). Electromagnetic wave propagation through terahertz chiral metamaterials. in 10th Photonics Workshop : Book of abstracts
Belgrade : Institute of physics., 9-9.
https://hdl.handle.net/21.15107/rcub_vinar_12789

Stojanović DB, Beličev P, Gligorić G, Radovanović JV, Milanović VB, Hadžievski L. Electromagnetic wave propagation through terahertz chiral metamaterials. in 10th Photonics Workshop : Book of abstracts. 2017;:9-9.
https://hdl.handle.net/21.15107/rcub_vinar_12789 .

Stojanović, Danka B., Beličev, Petra, Gligorić, Goran, Radovanović, Jelena V., Milanović, Vitomir B., Hadžievski, Ljupčo, "Electromagnetic wave propagation through terahertz chiral metamaterials" in 10th Photonics Workshop : Book of abstracts (2017):9-9,
https://hdl.handle.net/21.15107/rcub_vinar_12789 .

TY  - JOUR
AU  - Radosavljević, Ana
AU  - Gligorić, Goran
AU  - Beličev, Petra
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1658
AB  - By introducing evolving disorder in the binary kagome ribbons, we study the establishment of diffusive spreading of flat band states characterized by diffractionless propagation in regular periodic ribbons. Our numerical analysis relies on controlling strength and rate of change of disorder during light propagation while tailoring binarism of the kagome ribbons in order to isolate the flat band with the gap from the rest of the ribbons eigenvalue spectrum and study systematically its influence on diffusion. We show that the flat band plays a dominant role in the establishment of the diffusion for a given strength and rate of change of disorder, whereas the rest of the ribbons eigenvalue spectrum induces only quantitative differences in the light spreading regimes. Due to the universality of studied phenomena, our findings may be of interest in various disordered physical systems with flat spectral bands, ranging from photonics to ultracold matter systems and plasmonics.
T2  - Physical Review E
T1  - Light propagation in binary kagome ribbons with evolving disorder
VL  - 96
IS  - 1
DO  - 10.1103/PhysRevE.96.012225
ER  - 

@article{
author = "Radosavljević, Ana and Gligorić, Goran and Beličev, Petra and Maluckov, Aleksandra and Stepić, Milutin",
year = "2017",
abstract = "By introducing evolving disorder in the binary kagome ribbons, we study the establishment of diffusive spreading of flat band states characterized by diffractionless propagation in regular periodic ribbons. Our numerical analysis relies on controlling strength and rate of change of disorder during light propagation while tailoring binarism of the kagome ribbons in order to isolate the flat band with the gap from the rest of the ribbons eigenvalue spectrum and study systematically its influence on diffusion. We show that the flat band plays a dominant role in the establishment of the diffusion for a given strength and rate of change of disorder, whereas the rest of the ribbons eigenvalue spectrum induces only quantitative differences in the light spreading regimes. Due to the universality of studied phenomena, our findings may be of interest in various disordered physical systems with flat spectral bands, ranging from photonics to ultracold matter systems and plasmonics.",
journal = "Physical Review E",
title = "Light propagation in binary kagome ribbons with evolving disorder",
volume = "96",
number = "1",
doi = "10.1103/PhysRevE.96.012225"
}

Radosavljević, A., Gligorić, G., Beličev, P., Maluckov, A.,& Stepić, M.. (2017). Light propagation in binary kagome ribbons with evolving disorder. in Physical Review E, 96(1).
https://doi.org/10.1103/PhysRevE.96.012225

Radosavljević A, Gligorić G, Beličev P, Maluckov A, Stepić M. Light propagation in binary kagome ribbons with evolving disorder. in Physical Review E. 2017;96(1).
doi:10.1103/PhysRevE.96.012225 .

Radosavljević, Ana, Gligorić, Goran, Beličev, Petra, Maluckov, Aleksandra, Stepić, Milutin, "Light propagation in binary kagome ribbons with evolving disorder" in Physical Review E, 96, no. 1 (2017),
https://doi.org/10.1103/PhysRevE.96.012225 . .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Johansson, Magnus M.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1885
AB  - Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.
T2  - Physical Review A
T1  - Localized gap modes in nonlinear dimerized Lieb lattices
VL  - 96
IS  - 6
DO  - 10.1103/PhysRevA.96.063838
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin and Johansson, Magnus M.",
year = "2017",
abstract = "Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.",
journal = "Physical Review A",
title = "Localized gap modes in nonlinear dimerized Lieb lattices",
volume = "96",
number = "6",
doi = "10.1103/PhysRevA.96.063838"
}

Beličev, P., Gligorić, G., Maluckov, A., Stepić, M.,& Johansson, M. M.. (2017). Localized gap modes in nonlinear dimerized Lieb lattices. in Physical Review A, 96(6).
https://doi.org/10.1103/PhysRevA.96.063838

Beličev P, Gligorić G, Maluckov A, Stepić M, Johansson MM. Localized gap modes in nonlinear dimerized Lieb lattices. in Physical Review A. 2017;96(6).
doi:10.1103/PhysRevA.96.063838 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, Johansson, Magnus M., "Localized gap modes in nonlinear dimerized Lieb lattices" in Physical Review A, 96, no. 6 (2017),
https://doi.org/10.1103/PhysRevA.96.063838 . .

TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Petrović, Jovana S.
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10953
AB  - The use of ultracold quantum gases, in particular bosonic and fermionic condensates, for simulating fundamental effects originating in condensed-matter physics has drawn much interest [1]. One of these effects is the spin-orbit coupling (SOC). This effect plays a major role in many phenomena and applications, including spin and anomalous Hall effects [2], topological insulators [3], spintronics [4], etc. In contrast to the complex picture found in solids, the experimental and theoretical description of SOC effects in Bose-Einstein condensate (BEC) is much simpler [5]. This has motivated our study of the impact of SOC on the immiscibility-miscibility transition in the localized complexes in BEC, which can emulate the phase transition between insulating and conducting states in semiconductor. For this purpose, we introduce a discrete model for binary SO-coupled BEC trapped in a deep one-dimensional optical lattice [6]. We consider two different types of coupling, with spatial derivatives acting inside each species, and between the species. Stable localized composite states of miscible and immiscible types are found to exist for both types of coupling. We also study how the transition between miscible and immiscible type of localized complexes depends on the SOC strength. Particularly interesting are the applications of our model to the SOC binary condensates built of infinitely heavy atoms and the binary BEC with effective atomic masses which have opposite signs.
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
T1  - Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates
SP  - 48
EP  - 49
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10953
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Petrović, Jovana S. and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2015",
abstract = "The use of ultracold quantum gases, in particular bosonic and fermionic condensates, for simulating fundamental effects originating in condensed-matter physics has drawn much interest [1]. One of these effects is the spin-orbit coupling (SOC). This effect plays a major role in many phenomena and applications, including spin and anomalous Hall effects [2], topological insulators [3], spintronics [4], etc. In contrast to the complex picture found in solids, the experimental and theoretical description of SOC effects in Bose-Einstein condensate (BEC) is much simpler [5]. This has motivated our study of the impact of SOC on the immiscibility-miscibility transition in the localized complexes in BEC, which can emulate the phase transition between insulating and conducting states in semiconductor. For this purpose, we introduce a discrete model for binary SO-coupled BEC trapped in a deep one-dimensional optical lattice [6]. We consider two different types of coupling, with spatial derivatives acting inside each species, and between the species. Stable localized composite states of miscible and immiscible types are found to exist for both types of coupling. We also study how the transition between miscible and immiscible type of localized complexes depends on the SOC strength. Particularly interesting are the applications of our model to the SOC binary condensates built of infinitely heavy atoms and the binary BEC with effective atomic masses which have opposite signs.",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade",
title = "Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates",
pages = "48-49",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10953"
}

Beličev, P., Gligorić, G., Maluckov, A., Petrović, J. S., Hadžievski, L.,& Malomed, B. A.. (2015). Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 48-49.
https://hdl.handle.net/21.15107/rcub_vinar_10953

Beličev P, Gligorić G, Maluckov A, Petrović JS, Hadžievski L, Malomed BA. Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:48-49.
https://hdl.handle.net/21.15107/rcub_vinar_10953 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Petrović, Jovana S., Hadžievski, Ljupčo, Malomed, Boris A., "Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):48-49,
https://hdl.handle.net/21.15107/rcub_vinar_10953 .

TY  - CONF
AU  - Raičević, Nevena
AU  - Ivanović, Marija D.
AU  - Beličev, Petra
AU  - Maluckov, Aleksandra
AU  - Petrović, Jovana
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12012
AB  - In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = =       ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
T1  - Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor
SP  - 173
EP  - 173
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12012
ER  - 

@conference{
author = "Raičević, Nevena and Ivanović, Marija D. and Beličev, Petra and Maluckov, Aleksandra and Petrović, Jovana",
year = "2015",
abstract = "In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = =       ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade",
title = "Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor",
pages = "173-173",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12012"
}

Raičević, N., Ivanović, M. D., Beličev, P., Maluckov, A.,& Petrović, J.. (2015). Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 173-173.
https://hdl.handle.net/21.15107/rcub_vinar_12012

Raičević N, Ivanović MD, Beličev P, Maluckov A, Petrović J. Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:173-173.
https://hdl.handle.net/21.15107/rcub_vinar_12012 .

Raičević, Nevena, Ivanović, Marija D., Beličev, Petra, Maluckov, Aleksandra, Petrović, Jovana, "Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):173-173,
https://hdl.handle.net/21.15107/rcub_vinar_12012 .

TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Radosavljević, Ana
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Poblete, Rodrigo Andres Vicencio
AU  - Johansson, Magnus M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10954
AB  - One of the attractive two-dimensional [2D] lattice configurations is characterized by kagome geometry. The specific arrangement of its elements, i.e. waveguides, in the form of periodic hexagons renders completely flat the first energy band in linear case. As a consequence, the localized ring-like eigenmodes belonging to the lowest energy state propagate without diffraction through the system [1, 2]. Here we study kagome ribbon [3], which can be interpreted as one-dimensional counterpart of the standard 2D kagome lattice, and can be fabricated by dint of the direct femtosecond laser inscription [4, 5]. The existence, stability and dynamical properties of various localized modes in binary kagome ribbon with defocusing Kerr type of nonlinearity have been explored, both numerically and analytically. We derived the corresponding dispersion relation and the bandgap spectrum, confirmed the opening of mini-gaps in it and found several types of stable ring-like modes to exist: staggered, unstaggered and vortex. Beside these nonlinear mode configurations occurring in a semi-infinite gap, we investigated features of "hourglass" solutions, identified in [3] as interesting structures when kagome lattice dimensionality is reduced to 1D. In nonlinear binary kagome ribbon dynamically stable propagation of unstaggered rings, vortex modes with certain topological charge and hourglass solutions are observed, while the staggered ring solutions are destabilized. In addition, we examined possibility to generate stable propagating solitary modes inside the first mini-gap and found that these mode patterns localize within sites mutually coupled by smaller coupling constant. The last feature is opposite to the nonlinear localized solutions found in the semi-infinite gap.
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
T1  - On localized modes in nonlinear binary kagome ribbons
SP  - 68
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10954
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Radosavljević, Ana and Maluckov, Aleksandra and Stepić, Milutin and Poblete, Rodrigo Andres Vicencio and Johansson, Magnus M.",
year = "2015",
abstract = "One of the attractive two-dimensional [2D] lattice configurations is characterized by kagome geometry. The specific arrangement of its elements, i.e. waveguides, in the form of periodic hexagons renders completely flat the first energy band in linear case. As a consequence, the localized ring-like eigenmodes belonging to the lowest energy state propagate without diffraction through the system [1, 2]. Here we study kagome ribbon [3], which can be interpreted as one-dimensional counterpart of the standard 2D kagome lattice, and can be fabricated by dint of the direct femtosecond laser inscription [4, 5]. The existence, stability and dynamical properties of various localized modes in binary kagome ribbon with defocusing Kerr type of nonlinearity have been explored, both numerically and analytically. We derived the corresponding dispersion relation and the bandgap spectrum, confirmed the opening of mini-gaps in it and found several types of stable ring-like modes to exist: staggered, unstaggered and vortex. Beside these nonlinear mode configurations occurring in a semi-infinite gap, we investigated features of "hourglass" solutions, identified in [3] as interesting structures when kagome lattice dimensionality is reduced to 1D. In nonlinear binary kagome ribbon dynamically stable propagation of unstaggered rings, vortex modes with certain topological charge and hourglass solutions are observed, while the staggered ring solutions are destabilized. In addition, we examined possibility to generate stable propagating solitary modes inside the first mini-gap and found that these mode patterns localize within sites mutually coupled by smaller coupling constant. The last feature is opposite to the nonlinear localized solutions found in the semi-infinite gap.",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade",
title = "On localized modes in nonlinear binary kagome ribbons",
pages = "68",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10954"
}

Beličev, P., Gligorić, G., Radosavljević, A., Maluckov, A., Stepić, M., Poblete, R. A. V.,& Johansson, M. M.. (2015). On localized modes in nonlinear binary kagome ribbons. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 68.
https://hdl.handle.net/21.15107/rcub_vinar_10954

Beličev P, Gligorić G, Radosavljević A, Maluckov A, Stepić M, Poblete RAV, Johansson MM. On localized modes in nonlinear binary kagome ribbons. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:68.
https://hdl.handle.net/21.15107/rcub_vinar_10954 .

Beličev, Petra, Gligorić, Goran, Radosavljević, Ana, Maluckov, Aleksandra, Stepić, Milutin, Poblete, Rodrigo Andres Vicencio, Johansson, Magnus M., "On localized modes in nonlinear binary kagome ribbons" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):68,
https://hdl.handle.net/21.15107/rcub_vinar_10954 .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Petrović, Jovana S.
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/443
AB  - We introduce a discrete model for binary spin-orbit-coupled Bose-Einstein condensates trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the spin-orbit coupling (SOC), while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.
T2  - Journal of Physics. B: Atomic Molecular and Optical Physics
T1  - Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates
VL  - 48
IS  - 6
DO  - 10.1088/0953-4075/48/6/065301
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Petrović, Jovana S. and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2015",
abstract = "We introduce a discrete model for binary spin-orbit-coupled Bose-Einstein condensates trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the spin-orbit coupling (SOC), while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.",
journal = "Journal of Physics. B: Atomic Molecular and Optical Physics",
title = "Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates",
volume = "48",
number = "6",
doi = "10.1088/0953-4075/48/6/065301"
}

Beličev, P., Gligorić, G., Petrović, J. S., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2015). Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics, 48(6).
https://doi.org/10.1088/0953-4075/48/6/065301

Beličev P, Gligorić G, Petrović JS, Maluckov A, Hadžievski L, Malomed BA. Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics. 2015;48(6).
doi:10.1088/0953-4075/48/6/065301 .

Beličev, Petra, Gligorić, Goran, Petrović, Jovana S., Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates" in Journal of Physics. B: Atomic Molecular and Optical Physics, 48, no. 6 (2015),
https://doi.org/10.1088/0953-4075/48/6/065301 . .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Radosavljević, Ana
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Poblete, Rodrigo Andres Vicencio
AU  - Johansson, Magnus M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/838
AB  - The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the binarism. Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system binarism various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.
PB  - American Physical Society
T2  - Physical Review E
T1  - Localized modes in nonlinear binary kagome ribbons
VL  - 92
IS  - 5
DO  - 10.1103/PhysRevE.92.052916
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Radosavljević, Ana and Maluckov, Aleksandra and Stepić, Milutin and Poblete, Rodrigo Andres Vicencio and Johansson, Magnus M.",
year = "2015",
abstract = "The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the binarism. Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system binarism various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.",
publisher = "American Physical Society",
journal = "Physical Review E",
title = "Localized modes in nonlinear binary kagome ribbons",
volume = "92",
number = "5",
doi = "10.1103/PhysRevE.92.052916"
}

Beličev, P., Gligorić, G., Radosavljević, A., Maluckov, A., Stepić, M., Poblete, R. A. V.,& Johansson, M. M.. (2015). Localized modes in nonlinear binary kagome ribbons. in Physical Review E
American Physical Society., 92(5).
https://doi.org/10.1103/PhysRevE.92.052916

Beličev P, Gligorić G, Radosavljević A, Maluckov A, Stepić M, Poblete RAV, Johansson MM. Localized modes in nonlinear binary kagome ribbons. in Physical Review E. 2015;92(5).
doi:10.1103/PhysRevE.92.052916 .

Beličev, Petra, Gligorić, Goran, Radosavljević, Ana, Maluckov, Aleksandra, Stepić, Milutin, Poblete, Rodrigo Andres Vicencio, Johansson, Magnus M., "Localized modes in nonlinear binary kagome ribbons" in Physical Review E, 92, no. 5 (2015),
https://doi.org/10.1103/PhysRevE.92.052916 . .

TY  - JOUR
AU  - Beličev, Petra
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7055
AB  - Linear and nonlinear effects accompanying the propagation of visible laser light through geometrically different one-dimensional photonic lattices made of material with a saturable nonlinearity are investigated, both theoretically and experimentally. Existence, stability and dynamics of various types of nonlinear localized modes (solitons) found to occur in lattices with a defect are explored. Additionally, the phenomenon of spontaneous symmetry breaking of a certain type of solitons is observed in symmetric lattices comprising a defect.
T2  - Physica Scripta
T1  - Propagation of light in photonic lattices with saturable nonlinearity comprising a defect
VL  - T162
DO  - 10.1088/0031-8949/2014/T162/014001
ER  - 

@article{
author = "Beličev, Petra",
year = "2014",
abstract = "Linear and nonlinear effects accompanying the propagation of visible laser light through geometrically different one-dimensional photonic lattices made of material with a saturable nonlinearity are investigated, both theoretically and experimentally. Existence, stability and dynamics of various types of nonlinear localized modes (solitons) found to occur in lattices with a defect are explored. Additionally, the phenomenon of spontaneous symmetry breaking of a certain type of solitons is observed in symmetric lattices comprising a defect.",
journal = "Physica Scripta",
title = "Propagation of light in photonic lattices with saturable nonlinearity comprising a defect",
volume = "T162",
doi = "10.1088/0031-8949/2014/T162/014001"
}

Beličev, P.. (2014). Propagation of light in photonic lattices with saturable nonlinearity comprising a defect. in Physica Scripta, T162.
https://doi.org/10.1088/0031-8949/2014/T162/014001

Beličev P. Propagation of light in photonic lattices with saturable nonlinearity comprising a defect. in Physica Scripta. 2014;T162.
doi:10.1088/0031-8949/2014/T162/014001 .

Beličev, Petra, "Propagation of light in photonic lattices with saturable nonlinearity comprising a defect" in Physica Scripta, T162 (2014),
https://doi.org/10.1088/0031-8949/2014/T162/014001 . .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5765
AB  - We investigated the influence of the structural defect placed inside uniform photonic lattice on existence and dynamics of dark spatially localized defect modes. Depending on the strength of the defect and considering the lattice with defocusing saturable nonlinearity, we found two different types of dark solutions to exist. Their stability and dynamical properties are shown to be affected by the defect as well. Copyright (C) EPLA, 2013
T2  - Europhysics Letters / EPL
T1  - Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity
VL  - 104
IS  - 1
DO  - 10.1209/0295-5075/104/14006
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin",
year = "2013",
abstract = "We investigated the influence of the structural defect placed inside uniform photonic lattice on existence and dynamics of dark spatially localized defect modes. Depending on the strength of the defect and considering the lattice with defocusing saturable nonlinearity, we found two different types of dark solutions to exist. Their stability and dynamical properties are shown to be affected by the defect as well. Copyright (C) EPLA, 2013",
journal = "Europhysics Letters / EPL",
title = "Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity",
volume = "104",
number = "1",
doi = "10.1209/0295-5075/104/14006"
}

Beličev, P., Gligorić, G., Maluckov, A.,& Stepić, M.. (2013). Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity. in Europhysics Letters / EPL, 104(1).
https://doi.org/10.1209/0295-5075/104/14006

Beličev P, Gligorić G, Maluckov A, Stepić M. Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity. in Europhysics Letters / EPL. 2013;104(1).
doi:10.1209/0295-5075/104/14006 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, "Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity" in Europhysics Letters / EPL, 104, no. 1 (2013),
https://doi.org/10.1209/0295-5075/104/14006 . .

TY  - JOUR
AU  - Beličev, Petra
AU  - Ilic, Igor
AU  - Stepić, Milutin
AU  - Hadžievski, Ljupčo
AU  - Lou, Cibo
AU  - Suntsov, Sergiy
AU  - Rueter, Christian E.
AU  - Kip, Detlef
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5648
AB  - We observe theoretically and experimentally the phenomenon of spontaneous symmetry breaking of strongly localized nonlinear optical modes at the microwatt level in a one-dimensional photonic lattice with a single coupling defect.
T2  - Physical Review A
T1  - Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices
VL  - 88
IS  - 2
DO  - 10.1103/PhysRevA.88.023858
ER  - 

@article{
author = "Beličev, Petra and Ilic, Igor and Stepić, Milutin and Hadžievski, Ljupčo and Lou, Cibo and Suntsov, Sergiy and Rueter, Christian E. and Kip, Detlef",
year = "2013",
abstract = "We observe theoretically and experimentally the phenomenon of spontaneous symmetry breaking of strongly localized nonlinear optical modes at the microwatt level in a one-dimensional photonic lattice with a single coupling defect.",
journal = "Physical Review A",
title = "Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices",
volume = "88",
number = "2",
doi = "10.1103/PhysRevA.88.023858"
}

Beličev, P., Ilic, I., Stepić, M., Hadžievski, L., Lou, C., Suntsov, S., Rueter, C. E.,& Kip, D.. (2013). Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices. in Physical Review A, 88(2).
https://doi.org/10.1103/PhysRevA.88.023858

Beličev P, Ilic I, Stepić M, Hadžievski L, Lou C, Suntsov S, Rueter CE, Kip D. Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices. in Physical Review A. 2013;88(2).
doi:10.1103/PhysRevA.88.023858 .

Beličev, Petra, Ilic, Igor, Stepić, Milutin, Hadžievski, Ljupčo, Lou, Cibo, Suntsov, Sergiy, Rueter, Christian E., Kip, Detlef, "Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices" in Physical Review A, 88, no. 2 (2013),
https://doi.org/10.1103/PhysRevA.88.023858 . .

TY  - THES
AU  - Beličev, Petra
PY  - 2012
UR  - http://eteze.bg.ac.rs/application/showtheses?thesesId=215
UR  - https://fedorabg.bg.ac.rs/fedora/get/o:5471/bdef:Content/download
UR  - http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=43479055
UR  - http://nardus.mpn.gov.rs/123456789/2237
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7244
AB  - U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efektikoji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonskerešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, naprimer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali,moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dveuniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako unelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. Udoktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričkemetode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni ieksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćenimatematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina,tačnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostimaKerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenommetoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih utezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) iRunge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultatipokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom,tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanjenelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, unelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeniodgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju napostojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskojstrukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizommeđusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih napovršini rešetke.
AB  - In this dissertation the linear and nonlinear effects accompanying the propagationof visible laser light through a different one-dimensional (1D) photonic lattices made of materialwith a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are bothinvestigated, theoretically and experimentally. Due to the nonlinear response of these materialsto the intensity of incident radiation, the light passing through the photonic lattice causes localchange in the refractive index, providing necessary conditions for the formation of stablelocalized spatial structures at the interfaces between two uniform lattices of the same or differentperiods, and also within the binary superlattices, in the nonlinear regime, as well as in the linearregime when the localization occurs in the vicinity of the defect. In this dissertation, appropriatemathematical models are developed and various numerical methods for obtaining the relevantresults are applied. Some of the results have been confirmed experimentally in 1D nonlinearphotonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupleddifference- differential equations, namely the 1D discrete nonlinear Schrödinger equation withthe nonlinear term of Kerr and saturable type, while the stability of the obtained solutions wasinvestigated using the method of linear stability analysis. To solve stationary and dynamicequations presented in this dissertation, numerical methods such as the Gauss-Newton andRunge-Kutta methods are performed, respectively. The obtained numerical and experimentalresults show that the presence of the defect affects the formation of localized modes in thenonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation ofthe nonlinear response of the medium. Furthermore, the results indicate to the possibleappearance of the symmetry breaking of the mode profiles of certain nonlinear localizedsolutions when appropriate conditions are met. In the case of light propagation through binarysuperlattices, results show the emergence of new types of localized solutions and the opening ofan additional gap in the observed energy spectrum of the lattice. Additionally, numerical resultsobtained by analyzing the mutual interaction of soliton solutions, as well as examining theproperties of localized modes at the surface of the lattice, are presented as well.
PB  - Универзитет у Београду, Електротехнички факултет
T2  - Универзитет у Београду
T1  - Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću
T1  - Propagation of light in complex photonic lattices with saturable nonlinearity
UR  - https://hdl.handle.net/21.15107/rcub_nardus_2237
ER  - 

@phdthesis{
author = "Beličev, Petra",
year = "2012",
abstract = "U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efektikoji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonskerešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, naprimer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali,moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dveuniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako unelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. Udoktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričkemetode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni ieksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćenimatematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina,tačnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostimaKerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenommetoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih utezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) iRunge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultatipokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom,tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanjenelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, unelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeniodgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju napostojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskojstrukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizommeđusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih napovršini rešetke., In this dissertation the linear and nonlinear effects accompanying the propagationof visible laser light through a different one-dimensional (1D) photonic lattices made of materialwith a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are bothinvestigated, theoretically and experimentally. Due to the nonlinear response of these materialsto the intensity of incident radiation, the light passing through the photonic lattice causes localchange in the refractive index, providing necessary conditions for the formation of stablelocalized spatial structures at the interfaces between two uniform lattices of the same or differentperiods, and also within the binary superlattices, in the nonlinear regime, as well as in the linearregime when the localization occurs in the vicinity of the defect. In this dissertation, appropriatemathematical models are developed and various numerical methods for obtaining the relevantresults are applied. Some of the results have been confirmed experimentally in 1D nonlinearphotonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupleddifference- differential equations, namely the 1D discrete nonlinear Schrödinger equation withthe nonlinear term of Kerr and saturable type, while the stability of the obtained solutions wasinvestigated using the method of linear stability analysis. To solve stationary and dynamicequations presented in this dissertation, numerical methods such as the Gauss-Newton andRunge-Kutta methods are performed, respectively. The obtained numerical and experimentalresults show that the presence of the defect affects the formation of localized modes in thenonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation ofthe nonlinear response of the medium. Furthermore, the results indicate to the possibleappearance of the symmetry breaking of the mode profiles of certain nonlinear localizedsolutions when appropriate conditions are met. In the case of light propagation through binarysuperlattices, results show the emergence of new types of localized solutions and the opening ofan additional gap in the observed energy spectrum of the lattice. Additionally, numerical resultsobtained by analyzing the mutual interaction of soliton solutions, as well as examining theproperties of localized modes at the surface of the lattice, are presented as well.",
publisher = "Универзитет у Београду, Електротехнички факултет",
journal = "Универзитет у Београду",
title = "Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću, Propagation of light in complex photonic lattices with saturable nonlinearity",
url = "https://hdl.handle.net/21.15107/rcub_nardus_2237"
}

Beličev, P.. (2012). Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću. in Универзитет у Београду
Универзитет у Београду, Електротехнички факултет..
https://hdl.handle.net/21.15107/rcub_nardus_2237

Beličev P. Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću. in Универзитет у Београду. 2012;.
https://hdl.handle.net/21.15107/rcub_nardus_2237 .

Beličev, Petra, "Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću" in Универзитет у Београду (2012),
https://hdl.handle.net/21.15107/rcub_nardus_2237 .

TY  - JOUR
AU  - Ilic, I.
AU  - Beličev, Petra
AU  - Milanović, Vitomir B.
AU  - Radovanović, Jelena V.
AU  - Hadžievski, Ljupčo
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5135
AB  - The aspects of light propagation through a semiconductor metamaterial (SMM) which consists of two alternating differently doped In0.53Ga0.47As layers are studied analytically and numerically. A general analytical expression for the effective index of refraction of the Poynting vector is derived for periodic structure composed of two alternating layers of absorptive and dispersive semiconductors and light propagation is simulated by finite-difference-time-domain method. Negative values of the effective refractive index with low absorption are observed in the mid-infrared frequency range. The main advantage of this design is the possibility to control the frequency region with negative effective refractive index by changing the doping densities of the layers.
T2  - Journal of Electromagnetic Waves and Applications
T1  - Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities
VL  - 26
IS  - 17-18
SP  - 2323
EP  - 2331
DO  - 10.1080/09205071.2012.733507
ER  - 

@article{
author = "Ilic, I. and Beličev, Petra and Milanović, Vitomir B. and Radovanović, Jelena V. and Hadžievski, Ljupčo",
year = "2012",
abstract = "The aspects of light propagation through a semiconductor metamaterial (SMM) which consists of two alternating differently doped In0.53Ga0.47As layers are studied analytically and numerically. A general analytical expression for the effective index of refraction of the Poynting vector is derived for periodic structure composed of two alternating layers of absorptive and dispersive semiconductors and light propagation is simulated by finite-difference-time-domain method. Negative values of the effective refractive index with low absorption are observed in the mid-infrared frequency range. The main advantage of this design is the possibility to control the frequency region with negative effective refractive index by changing the doping densities of the layers.",
journal = "Journal of Electromagnetic Waves and Applications",
title = "Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities",
volume = "26",
number = "17-18",
pages = "2323-2331",
doi = "10.1080/09205071.2012.733507"
}

Ilic, I., Beličev, P., Milanović, V. B., Radovanović, J. V.,& Hadžievski, L.. (2012). Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities. in Journal of Electromagnetic Waves and Applications, 26(17-18), 2323-2331.
https://doi.org/10.1080/09205071.2012.733507

Ilic I, Beličev P, Milanović VB, Radovanović JV, Hadžievski L. Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities. in Journal of Electromagnetic Waves and Applications. 2012;26(17-18):2323-2331.
doi:10.1080/09205071.2012.733507 .

Ilic, I., Beličev, Petra, Milanović, Vitomir B., Radovanović, Jelena V., Hadžievski, Ljupčo, "Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities" in Journal of Electromagnetic Waves and Applications, 26, no. 17-18 (2012):2323-2331,
https://doi.org/10.1080/09205071.2012.733507 . .

TY  - JOUR
AU  - Radovanović, Jelena V.
AU  - Ilic, Igor
AU  - Beličev, Petra
AU  - Milanović, Vitomir B.
AU  - Hadžievski, Ljupčo
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5172
AB  - We present a comparative analysis of the tunneling times of electromagnetic (EM) waves propagating in isotropic and anisotropic media. First, suitable expressions for the tunneling times in a layered periodic material, with anisotropic properties originating from its structure, are derived, followed by numerical calculations performed for a new type of anisotropic semiconductor metamaterial. In the first case, we have considered a layered structure which contains two differently doped In0.53Ga0.47As semiconductor layers. The second structure under investigation is made of alternately placed layers of doped In0.53Ga0.47As and undoped Al0.48Ga0.52As. The investigation of the dwell time as a function of incident wave frequency has revealed the existence of two peaks, one of which may be interpreted as a consequence of anisotropy, while the other one corresponds to the peak related to the absorption and the group delay. Both of these two peaks are affected by variations of layers doping densities. Furthermore, at increased incident angles of incoming EM waves, the dwell time peak occurs at the upper boundary of the frequency interval, for which the structure exhibits negative refractive index.
T2  - Applied Physics. A: Materials Science and Processing
T1  - Comparison of tunneling times in isotropic and anisotropic media
VL  - 109
IS  - 4
SP  - 997
EP  - 1006
DO  - 10.1007/s00339-012-7393-5
ER  - 

@article{
author = "Radovanović, Jelena V. and Ilic, Igor and Beličev, Petra and Milanović, Vitomir B. and Hadžievski, Ljupčo",
year = "2012",
abstract = "We present a comparative analysis of the tunneling times of electromagnetic (EM) waves propagating in isotropic and anisotropic media. First, suitable expressions for the tunneling times in a layered periodic material, with anisotropic properties originating from its structure, are derived, followed by numerical calculations performed for a new type of anisotropic semiconductor metamaterial. In the first case, we have considered a layered structure which contains two differently doped In0.53Ga0.47As semiconductor layers. The second structure under investigation is made of alternately placed layers of doped In0.53Ga0.47As and undoped Al0.48Ga0.52As. The investigation of the dwell time as a function of incident wave frequency has revealed the existence of two peaks, one of which may be interpreted as a consequence of anisotropy, while the other one corresponds to the peak related to the absorption and the group delay. Both of these two peaks are affected by variations of layers doping densities. Furthermore, at increased incident angles of incoming EM waves, the dwell time peak occurs at the upper boundary of the frequency interval, for which the structure exhibits negative refractive index.",
journal = "Applied Physics. A: Materials Science and Processing",
title = "Comparison of tunneling times in isotropic and anisotropic media",
volume = "109",
number = "4",
pages = "997-1006",
doi = "10.1007/s00339-012-7393-5"
}

Radovanović, J. V., Ilic, I., Beličev, P., Milanović, V. B.,& Hadžievski, L.. (2012). Comparison of tunneling times in isotropic and anisotropic media. in Applied Physics. A: Materials Science and Processing, 109(4), 997-1006.
https://doi.org/10.1007/s00339-012-7393-5

Radovanović JV, Ilic I, Beličev P, Milanović VB, Hadžievski L. Comparison of tunneling times in isotropic and anisotropic media. in Applied Physics. A: Materials Science and Processing. 2012;109(4):997-1006.
doi:10.1007/s00339-012-7393-5 .

Radovanović, Jelena V., Ilic, Igor, Beličev, Petra, Milanović, Vitomir B., Hadžievski, Ljupčo, "Comparison of tunneling times in isotropic and anisotropic media" in Applied Physics. A: Materials Science and Processing, 109, no. 4 (2012):997-1006,
https://doi.org/10.1007/s00339-012-7393-5 . .

TY  - JOUR
AU  - Ilic, I.
AU  - Beličev, Petra
AU  - Milanović, Vitomir B.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6951
AB  - Tunneling times in an anisotropic structure composed of alternately placed layers of two linear, dispersive and absorptive materials are analyzed in this paper. For such a structure, a general expression for the relation between the two most common tunneling time definitions, namely the dwell time and the group delay, is obtained. Numerical calculations are performed for a new type of semiconductor metamaterial. The results show a peak position frequency mismatch between the dwell time and the group delay, and between the dwell time and the absorption.
T2  - Physica Scripta
T1  - Modeling of tunneling times in anisotropic non-magnetic metamaterials
VL  - T149
DO  - 10.1088/0031-8949/2012/T149/014050
ER  - 

@article{
author = "Ilic, I. and Beličev, Petra and Milanović, Vitomir B.",
year = "2012",
abstract = "Tunneling times in an anisotropic structure composed of alternately placed layers of two linear, dispersive and absorptive materials are analyzed in this paper. For such a structure, a general expression for the relation between the two most common tunneling time definitions, namely the dwell time and the group delay, is obtained. Numerical calculations are performed for a new type of semiconductor metamaterial. The results show a peak position frequency mismatch between the dwell time and the group delay, and between the dwell time and the absorption.",
journal = "Physica Scripta",
title = "Modeling of tunneling times in anisotropic non-magnetic metamaterials",
volume = "T149",
doi = "10.1088/0031-8949/2012/T149/014050"
}

Ilic, I., Beličev, P.,& Milanović, V. B.. (2012). Modeling of tunneling times in anisotropic non-magnetic metamaterials. in Physica Scripta, T149.
https://doi.org/10.1088/0031-8949/2012/T149/014050

Ilic I, Beličev P, Milanović VB. Modeling of tunneling times in anisotropic non-magnetic metamaterials. in Physica Scripta. 2012;T149.
doi:10.1088/0031-8949/2012/T149/014050 .

Ilic, I., Beličev, Petra, Milanović, Vitomir B., "Modeling of tunneling times in anisotropic non-magnetic metamaterials" in Physica Scripta, T149 (2012),
https://doi.org/10.1088/0031-8949/2012/T149/014050 . .